Analyse en composantes principales

Préparation de l’analyse

Packages

library(tidyverse)  # Manipulation des données
library(readxl)     # Lecture des fichiers Excel
library(ggpubr)     # Représentations graphiques
library(rstatix)    # Tests statistiques en langage Dplyr
library(FactoMineR) # Analyses en composantes principales
library(factoextra) # Visualisation graphique de l'ACP
library(gtsummary)  # Résumé descriptif des données
library(corrplot)
library(plotly)

Importation des données

data <- read_excel("data/data_ubs.xlsx", sheet = "reponses") %>% select(-ID)


head(data)

Résumé descriptif des données

Cliquer pour afficher

Characteristic	N = 1821
LDS2
1	7 (3.8%)
2	12 (6.6%)
3	46 (25%)
4	79 (43%)
5	38 (21%)
LDS3
1	3 (1.6%)
2	12 (6.6%)
3	122 (67%)
4	35 (19%)
5	10 (5.5%)
LDS4
1	7 (3.8%)
2	19 (10%)
3	95 (52%)
4	49 (27%)
5	12 (6.6%)
LDS5
1	5 (2.7%)
2	27 (15%)
3	62 (34%)
4	57 (31%)
5	31 (17%)
LDS6
1	28 (15%)
2	41 (23%)
3	69 (38%)
4	37 (20%)
5	7 (3.8%)
NSUB1
1	3 (1.6%)
2	4 (2.2%)
3	75 (41%)
4	72 (40%)
5	28 (15%)
NSUB2
1	21 (12%)
2	58 (32%)
3	84 (46%)
4	16 (8.8%)
5	3 (1.6%)
NSUB3
1	39 (21%)
2	59 (32%)
3	45 (25%)
4	31 (17%)
5	8 (4.4%)
NSUB4
1	20 (11%)
2	29 (16%)
3	47 (26%)
4	57 (31%)
5	29 (16%)
NSUB5
1	8 (4.4%)
2	15 (8.2%)
3	43 (24%)
4	70 (38%)
5	46 (25%)
CF1
1	2 (1.1%)
2	6 (3.3%)
3	24 (13%)
4	83 (46%)
5	67 (37%)
CF2
1	14 (7.7%)
2	49 (27%)
3	45 (25%)
4	63 (35%)
5	11 (6.0%)
CF3
1	97 (53%)
2	54 (30%)
3	23 (13%)
4	5 (2.7%)
5	3 (1.6%)
CF4
1	1 (0.5%)
2	4 (2.2%)
3	10 (5.5%)
4	49 (27%)
5	118 (65%)
CF5
2	2 (1.1%)
3	8 (4.4%)
4	64 (35%)
5	108 (59%)
CF6
1	5 (2.7%)
2	16 (8.8%)
3	65 (36%)
4	49 (27%)
5	47 (26%)
CF7
1	2 (1.1%)
2	8 (4.4%)
3	39 (21%)
4	84 (46%)
5	49 (27%)
CF8
1	7 (3.8%)
2	24 (13%)
3	48 (26%)
4	79 (43%)
5	24 (13%)
AFE1
1	5 (2.7%)
2	13 (7.1%)
3	92 (51%)
4	39 (21%)
5	33 (18%)
AFE2
1	20 (11%)
2	40 (22%)
3	76 (42%)
4	33 (18%)
5	13 (7.1%)
AFE4
1	9 (4.9%)
2	16 (8.8%)
3	28 (15%)
4	51 (28%)
5	78 (43%)
AFE5
1	7 (3.8%)
2	25 (14%)
3	41 (23%)
4	71 (39%)
5	38 (21%)
APF1
1	3 (1.6%)
2	14 (7.7%)
3	92 (51%)
4	44 (24%)
5	29 (16%)
APF2
1	13 (7.1%)
2	22 (12%)
3	86 (47%)
4	40 (22%)
5	21 (12%)
APF3
2	9 (4.9%)
3	27 (15%)
4	62 (34%)
5	84 (46%)
APF4
2	3 (1.6%)
3	11 (6.0%)
4	66 (36%)
5	102 (56%)
APF5
1	1 (0.5%)
2	4 (2.2%)
3	19 (10%)
4	52 (29%)
5	106 (58%)
APF6
1	3 (1.6%)
2	13 (7.1%)
3	89 (49%)
4	55 (30%)
5	22 (12%)
IEIP1
2	1 (0.5%)
3	5 (2.7%)
4	86 (47%)
5	90 (49%)
IEIP2
1	2 (1.1%)
2	6 (3.3%)
3	12 (6.6%)
4	52 (29%)
5	110 (60%)
IEIP3
1	2 (1.1%)
2	14 (7.7%)
3	33 (18%)
4	70 (38%)
5	63 (35%)
IEIP4
1	36 (20%)
2	56 (31%)
3	51 (28%)
4	21 (12%)
5	18 (9.9%)
MOT1
1	2 (1.1%)
2	15 (8.2%)
3	85 (47%)
4	54 (30%)
5	26 (14%)
MOT2
1	1 (0.5%)
2	3 (1.6%)
3	19 (10%)
4	106 (58%)
5	53 (29%)
MOT3
2	4 (2.2%)
3	7 (3.8%)
4	91 (50%)
5	80 (44%)
MOT4
1	6 (3.3%)
2	19 (10%)
3	73 (40%)
4	55 (30%)
5	29 (16%)
MOT5
2	7 (3.8%)
3	41 (23%)
4	88 (48%)
5	46 (25%)
MOT6
1	2 (1.1%)
3	4 (2.2%)
4	47 (26%)
5	129 (71%)
MOT7
2	1 (0.5%)
3	16 (8.8%)
4	84 (46%)
5	81 (45%)
MOT8
2	1 (0.5%)
3	2 (1.1%)
4	53 (29%)
5	126 (69%)
MOT9
1	5 (2.7%)
2	3 (1.6%)
3	29 (16%)
4	71 (39%)
5	74 (41%)
INTU1
1	4 (2.2%)
2	6 (3.3%)
3	39 (21%)
4	77 (42%)
5	56 (31%)
1 n (%)

Analyse en composantes principales

res.pca <- PCA(data, scale.unit = T, graph = F)
print(res.pca)

**Results for the Principal Component Analysis (PCA)**
The analysis was performed on 182 individuals, described by 42 variables
*The results are available in the following objects:

   name               description                          
1  "$eig"             "eigenvalues"                        
2  "$var"             "results for the variables"          
3  "$var$coord"       "coord. for the variables"           
4  "$var$cor"         "correlations variables - dimensions"
5  "$var$cos2"        "cos2 for the variables"             
6  "$var$contrib"     "contributions of the variables"     
7  "$ind"             "results for the individuals"        
8  "$ind$coord"       "coord. for the individuals"         
9  "$ind$cos2"        "cos2 for the individuals"           
10 "$ind$contrib"     "contributions of the individuals"   
11 "$call"            "summary statistics"                 
12 "$call$centre"     "mean of the variables"              
13 "$call$ecart.type" "standard error of the variables"    
14 "$call$row.w"      "weights for the individuals"        
15 "$call$col.w"      "weights for the variables"          

Valeurs propres & Variances

eig.val <- get_eigenvalue(res.pca)
head(eig.val, 30)

       eigenvalue variance.percent cumulative.variance.percent
Dim.1   9.2402024       22.0004820                    22.00048
Dim.2   2.4639492        5.8665456                    27.86703
Dim.3   2.3166215        5.5157656                    33.38279
Dim.4   2.1244777        5.0582801                    38.44107
Dim.5   1.7006938        4.0492711                    42.49034
Dim.6   1.5799665        3.7618251                    46.25217
Dim.7   1.5150096        3.6071658                    49.85934
Dim.8   1.3376258        3.1848233                    53.04416
Dim.9   1.2928697        3.0782611                    56.12242
Dim.10  1.1820698        2.8144519                    58.93687
Dim.11  1.0698838        2.5473424                    61.48421
Dim.12  1.0204833        2.4297221                    63.91394
Dim.13  0.9394521        2.2367907                    66.15073
Dim.14  0.9333435        2.2222464                    68.37297
Dim.15  0.8877470        2.1136834                    70.48666
Dim.16  0.8124980        1.9345190                    72.42118
Dim.17  0.7878440        1.8758191                    74.29699
Dim.18  0.7495784        1.7847106                    76.08171
Dim.19  0.7310817        1.7406706                    77.82238
Dim.20  0.6748913        1.6068840                    79.42926
Dim.21  0.6462363        1.5386579                    80.96792
Dim.22  0.6381290        1.5193548                    82.48727
Dim.23  0.5740157        1.3667040                    83.85398
Dim.24  0.5588069        1.3304926                    85.18447
Dim.25  0.5501361        1.3098479                    86.49432
Dim.26  0.5156254        1.2276796                    87.72200
Dim.27  0.4873573        1.1603745                    88.88237
Dim.28  0.4632245        1.1029156                    89.98529
Dim.29  0.4501937        1.0718898                    91.05718
Dim.30  0.4163010        0.9911929                    92.04837

La proportion de variance expliquée par chaque valeur propre est donnée dans la deuxième colonne.

Une valeur propre > 1 indique que la composante principale (PC) concernée représente plus de variance par rapport à une seule variable d’origine, lorsque les données sont standardisées.

fviz_eig(res.pca, addlabels = TRUE)

Cercle des corrélations

fviz_pca_var(res.pca, col.var = "black", repel = T, alpha.var = 1)

Qualité de représentation

fviz_cos2(res.pca, choice = "var", axes = 1:2)

Un cos2 élevé indique une bonne représentation de la variable sur les axes principaux en considération.

Un faible cos2 indique que la variable n’est pas parfaitement représentée par les axes principaux.

Contributions des variables aux axes

fviz_contrib(res.pca, choice = "var", axes = 1, top = 40)

fviz_contrib(res.pca, choice = "var", axes = 2, top = 40)

La ligne en pointillé rouge, sur le graphique ci-dessus, indique la contribution moyenne attendue.

Individus

var <- get_pca_var(res.pca)
res.pca$ind.sup

NULL

p <- fviz_pca_ind(res.pca, col.ind.sup = "blue", label  =F)
p

Clustering

Identification du nombre optimal de clusters

fviz_nbclust(data, FUNcluster =factoextra::hcut, method = "gap_stat",hc_method = "average", hc_metric = "euclidean", stand = TRUE)

Clustering k = 1,2,..., K.max (= 10): .. done
Bootstrapping, b = 1,2,..., B (= 100)  [one "." per sample]:
.................................................. 50 
.................................................. 100 

library(NbClust)
NbClust(data, distance = "euclidean", method = "average")

Avis : Production de NaN

[1] "Frey index : No clustering structure in this data set"
*** : The Hubert index is a graphical method of determining the number of clusters.
                In the plot of Hubert index, we seek a significant knee that corresponds to a 
                significant increase of the value of the measure i.e the significant peak in Hubert
                index second differences plot. 
 

*** : The D index is a graphical method of determining the number of clusters. 
                In the plot of D index, we seek a significant knee (the significant peak in Dindex
                second differences plot) that corresponds to a significant increase of the value of
                the measure. 
 
******************************************************************* 
* Among all indices:                                                
* 8 proposed 2 as the best number of clusters 
* 2 proposed 3 as the best number of clusters 
* 1 proposed 5 as the best number of clusters 
* 10 proposed 6 as the best number of clusters 
* 1 proposed 10 as the best number of clusters 
* 1 proposed 15 as the best number of clusters 

                   ***** Conclusion *****                            
 
* According to the majority rule, the best number of clusters is  6 
 
 
******************************************************************* 
$All.index
        KL     CH Hartigan     CCC    Scott      Marriot   TrCovW   TraceW Friedman   Rubin Cindex     DB
2   3.2766 3.5156   2.7523 23.3208 1169.675 1.263789e+83 39723.23 6225.061 1944.474 18.2281 0.4872 0.5304
3   1.1437 3.1432   3.1258  7.4468 1308.251 1.327959e+83 38717.97 6131.311 1990.127 18.5068 0.4848 0.5764
4   2.1907 3.1563   2.1992  4.6237 1423.996 1.249871e+83 37250.38 6026.079 2012.857 18.8300 0.4814 1.0014
5   0.0326 2.9297  11.0933  3.0574 1563.043 9.096803e+82 36585.58 5952.534 2059.232 19.0626 0.4796 0.9339
6  17.7039 4.6827   1.8340  3.1575 1733.564 5.132715e+82 31175.80 5601.468 2106.146 20.2574 0.5092 1.2135
7   0.1937 4.2245   3.9152  2.4651 1846.424 3.757775e+82 30723.11 5543.702 2146.265 20.4685 0.5091 1.1139
8   2.5318 4.2369   2.0840  2.1889 1958.871 2.645998e+82 29601.86 5422.388 2163.131 20.9264 0.5323 1.1787
9   1.9044 3.9892   1.4488  1.7080 2072.950 1.789264e+82 29109.91 5358.214 2191.129 21.1770 0.5304 1.1214
10  0.3096 3.7150   2.6600  1.0127 2131.510 1.601230e+82 28707.88 5313.714 2203.475 21.3544 0.5304 0.9958
11  1.5226 3.6399   1.9443  0.5684 2256.854 9.730556e+81 27896.85 5232.787 2236.226 21.6846 0.5269 1.0415
12  0.3673 3.5028   4.0553 -0.0648 2328.865 7.796142e+81 27271.81 5173.958 2249.323 21.9312 0.5252 1.0123
13  1.9631 3.6041   2.3395 -0.2482 2457.708 4.507689e+81 26049.83 5053.410 2280.927 22.4543 0.5410 1.0859
14  1.4957 3.5319   1.7184 -0.7808 2601.444 2.373216e+81 25662.22 4984.410 2326.307 22.7652 0.5408 1.1084
15  0.9180 3.4154   1.7854 -1.4354 2716.095 1.451040e+81 25289.57 4933.944 2372.608 22.9980 0.5407 1.0452
   Silhouette   Duda Pseudot2   Beale Ratkowsky      Ball Ptbiserial    Frey McClain   Dunn Hubert SDindex
2      0.3384 0.9993   0.1189  0.0197    0.0806 3112.5304     0.2519 16.4275  0.0073 0.5496 0.0017  0.3251
3      0.2759 0.9828   3.1084  0.5175    0.0975 2043.7704     0.3093 14.6894  0.0153 0.5496 0.0016  0.2682
4      0.1888 1.0034  -0.5887 -0.0991    0.1079 1506.5197     0.3511  6.0721  0.0330 0.4380 0.0016  0.4176
5      0.1718 0.9406  11.0558  1.8719    0.1082 1190.5068     0.3732  2.2771  0.0421 0.4380 0.0015  0.3625
6      0.1593 1.0538  -0.4081 -1.3513    0.1400  933.5780     0.5326  1.3989  0.1382 0.4191 0.0015  0.4439
7      0.1578 0.9767   3.9430  0.7078    0.1355  791.9574     0.5333  1.4344  0.1388 0.4191 0.0015  0.4032
8      0.1416 1.0051  -0.8198 -0.1499    0.1362  677.7985     0.5648  1.1836  0.1715 0.4411 0.0015  0.4315
9      0.1427 4.7068   0.0000  0.0000    0.1325  595.3571     0.5751  1.8994  0.1828 0.4411 0.0015  0.4092
10     0.1357 0.9836   2.6823  0.4934    0.1284  531.3714     0.5751  1.6997  0.1829 0.4411 0.0015  0.3572
11     0.1327 1.0047  -0.7484 -0.1394    0.1268  475.7079     0.5887  1.6161  0.2065 0.4411 0.0015  0.3819
12     0.1266 0.9747   4.1048  0.7693    0.1246  431.1632     0.5949  1.4448  0.2186 0.4411 0.0014  0.3698
13     0.1181 0.7710   2.0789  7.7438    0.1256  388.7239     0.6176  1.3088  0.2688 0.4588 0.0015  0.4141
14     0.1168 1.1976  -0.6599 -3.9332    0.1247  356.0293     0.6182  1.7679  0.2703 0.4588 0.0014  0.4205
15     0.1194 1.0083  -1.2624 -0.2427    0.1231  328.9296     0.6183  1.8724  0.2707 0.4588 0.0014  0.4060
   Dindex   SDbw
2  5.6610 0.4943
3  5.6076 0.3274
4  5.5643 0.6072
5  5.5169 0.4846
6  5.3817 0.5767
7  5.3395 0.4865
8  5.2878 0.5886
9  5.2435 0.5227
10 5.1916 0.3244
11 5.1544 0.3953
12 5.1121 0.3619
13 5.0616 0.4086
14 5.0271 0.4274
15 4.9866 0.3911

$All.CriticalValues
   CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
2          0.9334            12.7635       1.0000
3          0.9333            12.7213       0.9959
4          0.9330            12.6367       1.0000
5          0.9329            12.5943       0.0006
6          0.7662             2.4416       1.0000
7          0.9313            12.1659       0.9221
8          0.9308            12.0357       1.0000
9          0.4959             0.0000          NaN
10         0.9307            11.9922       0.9976
11         0.9303            11.9048       1.0000
12         0.9302            11.8610       0.8588
13         0.7543             2.2797       0.0000
14         0.7025             1.6937       1.0000
15         0.9295            11.6848       1.0000

$Best.nc
                     KL     CH Hartigan     CCC    Scott      Marriot   TrCovW  TraceW Friedman   Rubin
Number_clusters  6.0000 6.0000   6.0000  2.0000   6.0000 6.000000e+00    6.000   6.000   6.0000  6.0000
Value_Index     17.7039 4.6827   9.2593 23.3208 170.5215 2.589147e+82 5409.783 293.299  46.9139 -0.9836
                Cindex     DB Silhouette   Duda PseudoT2  Beale Ratkowsky    Ball PtBiserial Frey McClain
Number_clusters 5.0000 2.0000     2.0000 2.0000   2.0000 2.0000      6.00    3.00    15.0000   NA  2.0000
Value_Index     0.4796 0.5304     0.3384 0.9993   0.1189 0.0197      0.14 1068.76     0.6183   NA  0.0073
                  Dunn Hubert SDindex Dindex    SDbw
Number_clusters 2.0000      0  3.0000      0 10.0000
Value_Index     0.5496      0  0.2682      0  0.3244

$Best.partition
  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [53] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[105] 1 1 1 1 5 1 1 1 5 1 1 1 1 1 1 5 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5 1 1 1 4 1
[157] 1 1 1 1 5 1 5 1 1 1 1 1 1 1 6 1 1 1 1 1 5 1 1 1 1 1

L’analyse recommande l’usage de 6 clusters

Clusters

Avec 6 clusters

res.km <- kmeans(scale(data), 6, nstart = 25)
print(res.km)

K-means clustering with 6 clusters of sizes 11, 21, 34, 14, 62, 40

Cluster means:
        LDS2        LDS3       LDS4        LDS5        LDS6        NSUB1       NSUB2       NSUB3       NSUB4
1 -0.6203445 -0.79746695 -1.5164796  0.09237398  0.57724912  0.205603410 -0.44852834 -0.84525990 -0.65308518
2 -0.6638071 -0.15199884 -0.4746705 -0.39218428  0.05831744 -0.554322920  0.71266170  0.18382864 -0.83018378
3  0.4695432  0.12775177  0.6304840 -0.06637771 -0.67226490  0.069649044 -0.52240360 -0.05662833 -0.01428008
4 -0.4964762 -0.48691154 -0.3369313 -0.02139187 -0.36534162 -0.006651875  0.16446039 -0.31928131 -0.08991160
5  0.3733359  0.25853931  0.1189410  0.33071141  0.19138523  0.249981755  0.01061035  0.05196514  0.45303846
6 -0.2849222 -0.03980309  0.0638898 -0.26820057  0.21328747 -0.209866657  0.11923378  0.21527301 -0.04315757
        NSUB5        CF1        CF2         CF3        CF4         CF5        CF6         CF7         CF8
1 -0.84367066  0.5897871  0.8841169  0.33154068  0.2597260 -0.11454882  0.6025497 -0.55075123 -0.57599062
2  0.03941804 -0.5000497 -0.4369773 -0.34761538  0.3060182 -0.08055031 -0.7516341  0.02103564  0.08185913
3  0.34478182  0.9152935 -0.8838180 -0.31381123  0.4670197  0.69601559  0.9043726  0.81890499  0.68280146
4 -0.87405215 -1.5975615  0.2896245  0.48826899 -2.1445754 -1.61388297 -1.2299467 -1.15485649 -0.41475293
5  0.29240113  0.1235984  0.3322405 -0.02236198  0.3008850  0.31152925  0.1564986  0.20540282  0.07499353
6 -0.22905308 -0.3100958  0.1211850  0.22183085 -0.3448213 -0.43583471 -0.3519014 -0.46983096 -0.43603631
         AFE1        AFE2        AFE4        AFE5        APF1        APF2        APF3       APF4       APF5
1  0.38266907  0.79651748  0.19656433  0.20773509 -0.09577480 -0.09320171  0.27451845  0.7763535 -0.0667380
2 -0.46897758 -0.25102655  0.48723614 -0.76846596 -0.54896209 -0.55176709  0.02720453 -0.1253904  0.3081483
3  0.72499763 -0.14114515  0.19201920  0.29422349  0.96198958  0.76168986  0.62890475  0.6478244  0.6113651
4 -0.84072811  0.31161917 -0.07938991  0.04570172 -0.96875663 -0.73687605 -1.38743109 -1.2005467 -1.1351639
5  0.06826188  0.03283729  0.09686473  0.12236267  0.05449256  0.02221997  0.28959662  0.1889893  0.2615898
6 -0.28681983 -0.12724449 -0.59542436 -0.10943023 -0.24854662 -0.10866252 -0.58761788 -0.5710600 -0.6712421
         APF6      IEIP1      IEIP2      IEIP3      IEIP4         MOT1        MOT2       MOT3       MOT4
1  0.22972852  0.1538282 -0.4132505 -0.2588015  1.2983792  0.076834942 -0.06603691  0.1467058 -0.9151228
2 -0.67985647 -0.9484638  0.3256272 -0.3213538 -0.5430886 -0.002086875 -0.26296418  0.1793071 -0.1185148
3  1.06619000  0.4298393  0.4899732  0.9637278 -0.0664734  1.164476230  0.85000069  0.7467612  0.7934392
4 -1.01337097 -0.1701563 -1.1136451 -1.5254853  0.1452270 -0.951614984 -1.00759541 -1.7213479 -1.0333009
5  0.05172371  0.2976211  0.4157524  0.2390945 -0.2106670 -0.177115098  0.14865749  0.1422888  0.1967680
6 -0.33800411 -0.3114806 -0.7284281 -0.4159641  0.2602741 -0.402245149 -0.44404495 -0.3873033 -0.3038794
        MOT5       MOT6        MOT7        MOT8       MOT9      INTU1
1  0.5192468  0.4013871  0.43874264  0.45327911  0.3466459  0.1399222
2 -0.4765518 -0.0547227  0.05260884 -0.09735702  0.1141177 -0.6279392
3  1.0603581  0.4980952  0.81063223  0.62586656  0.8378274  1.0277275
4 -1.3744029 -0.1296064 -1.17123897 -0.86578207 -2.0600208 -1.8125058
5  0.1838033  0.2399809  0.23258646  0.38090373  0.1182432  0.1637102
6 -0.5977617 -0.8316410 -0.78788664 -0.89290296 -0.3296624 -0.2017527

Clustering vector:
  [1] 3 2 1 6 5 1 3 5 6 1 3 6 6 6 3 5 6 1 5 6 2 6 3 3 1 3 5 3 5 2 2 6 4 3 5 5 3 5 5 6 3 6 5 6 2 6 6 1 5 5 5 5
 [53] 6 6 5 5 5 6 3 3 5 5 3 6 5 5 5 2 4 5 5 3 2 6 6 5 6 6 6 3 1 3 6 5 2 2 5 5 5 2 2 2 5 6 6 6 5 5 3 3 6 5 2 5
[105] 6 3 5 5 4 2 6 2 4 5 2 5 2 6 5 4 5 3 5 1 5 4 5 4 3 1 3 6 2 5 3 3 5 1 5 2 5 3 2 6 1 5 6 5 6 4 4 3 5 2 3 5
[157] 5 6 5 6 4 5 4 5 5 3 6 3 5 3 4 5 4 3 5 6 6 3 3 5 4 5

Within cluster sum of squares by cluster:
[1]  419.2851  612.0461 1058.3710  665.2583 1644.1213 1197.8989
 (between_SS / total_SS =  26.4 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss" "betweenss"    "size"        
[8] "iter"         "ifault"      

clust6p <- fviz_cluster(res.km, data = scale(data), 
             geom = "point",
             ellipse.type = "convex", 
             ggtheme = theme_bw()
             )
ggplotly(clust6p)

NA

Avec 2 clusters

res.km2 <- kmeans(scale(data %>% select(-clust6)), 2, nstart = 25)
print(res.km2)

K-means clustering with 2 clusters of sizes 69, 113

Cluster means:
        LDS2        LDS3      LDS4       LDS5        LDS6      NSUB1      NSUB2       NSUB3      NSUB4
1 -0.4788077 -0.16364798 -0.203983 -0.2833648  0.06025638 -0.2410100  0.2597997  0.12914277 -0.1712230
2  0.2923693  0.09992664  0.124556  0.1730280 -0.03679372  0.1471654 -0.1586388 -0.07885709  0.1045521
       NSUB5        CF1          CF2        CF3        CF4        CF5        CF6        CF7        CF8
1 -0.2666865 -0.6591094 -0.013844243  0.2202409 -0.5961766 -0.6464037 -0.6565658 -0.5068674 -0.3129629
2  0.1628440  0.4024650  0.008453564 -0.1344834  0.3640371  0.3947067  0.4009118  0.3095031  0.1911012
        AFE1        AFE2       AFE4       AFE5       APF1       APF2       APF3       APF4       APF5
1 -0.5142342 -0.09642129 -0.2536010 -0.2001750 -0.4964878 -0.3646461 -0.6422635 -0.6380877 -0.6062483
2  0.3140014  0.05887672  0.1548537  0.1222308  0.3031651  0.2226600  0.3921786  0.3896287  0.3701870
        APF6      IEIP1      IEIP2      IEIP3       IEIP4       MOT1       MOT2       MOT3       MOT4
1 -0.5469340 -0.4105945 -0.5381816 -0.5906006  0.07083764 -0.4455932 -0.5249096 -0.6034073 -0.3822746
2  0.3339686  0.2507170  0.3286241  0.3606322 -0.04325484  0.2720879  0.3205200  0.3684522  0.2334243
        MOT5       MOT6       MOT7       MOT8       MOT9      INTU1
1 -0.7576182 -0.5723969 -0.6986021 -0.7223165 -0.6243109 -0.6637673
2  0.4626164  0.3495167  0.4265800  0.4410605  0.3812164  0.4053092

Clustering vector:
  [1] 2 1 2 1 2 2 2 2 1 2 2 1 1 1 2 2 1 2 2 1 1 1 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 2 1 2 1 1 1 1 2 2 2 1 2
 [53] 1 1 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 1 1 2 1 1 1 2 2 2 1 2 1 2 2 2 2 1 2 1 2 1 1 1 2 2 2 2 1 2 1 2
[105] 1 2 2 2 1 1 1 1 1 2 1 2 1 1 2 1 2 2 2 2 2 1 2 1 2 2 2 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 1 2 1 1 1 2 2 2 2 2
[157] 2 1 2 1 1 2 1 2 2 2 1 2 2 2 1 2 1 2 2 1 1 2 2 2 1 2

Within cluster sum of squares by cluster:
[1] 2663.731 3888.215
 (between_SS / total_SS =  13.8 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss" "betweenss"    "size"        
[8] "iter"         "ifault"      

clust6p <- fviz_cluster(res.km2, data = scale(data %>% select(-clust6)), 
             geom = "point",
             ellipse.type = "convex", 
             ggtheme = theme_bw()
             )
ggplotly(clust6p)

NA